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A posteriori error analysis of nonconforming finite volume elements for general second-order elliptic PDEs

✍ Scribed by Min Yang

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
148 KB
Volume
27
Category
Article
ISSN
0749-159X

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✦ Synopsis

Abstract

In this article, we study the a posteriori H^1^ and L^2^ error estimates for Crouzeix‐Raviart nonconforming finite volume element discretization of general second‐order elliptic problems in ℝ^2^. The error estimators yield global upper and local lower bounds. Finally, numerical experiments are performed to illustrate the theoretical findings. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011

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## Abstract We treat the finite volume element method (FVE) for solving general second order elliptic problems as a perturbation of the linear finite element method (FEM), and obtain the optimal __H__^1^ error estimate, __H__^1^ superconvergence and __L__^__p__^ (1 < __p__ ≤ ∞) error estimates betw